Random Effects Cox Models: A Poisson Modelling Approach
Renjun Ma$^{0,1}$, Daniel Krewski$^{1,2}$ and Richard T. Burnett$^{1,3}$
¹Faculty of Medicine, University of Ottawa, Ottawa, Canada, K1H 8M5
² School of Mathematics and Statistics, Carleton University, Ottawa, Canada, K1S 5B6
³ Environmental Health Directorate, Health Canada, Ottawa, Canada, K1A 0L2
February 1, 2000
Abstract
We propose a Poisson modelling approach to random effects Cox proportional hazards models. Specifically we describe methods of statistical inference for a class of random effects Cox models which accommodate a wide range of nested random effects distributions. The orthodox BLUP approach to random effects Poisson modeling techniques enables us to study this new class of models as a single class, rather than as a collection of unrelated models. The explicit expressions for the random effects given by our approach facilitate incorporation of relatively large number of random effects. An important feature of this approach is that the principal results depend only on the first and second moments of the unobserved random effects. The application of proposed methods is illustrated through the re-analysis of data on the time to failure (tumour onset) in an animal carcinogenesis experiment previously reported by Mantel and Ciminera (1979).
Key words: Cox model; BLUP; estimating equation; frailty; generalized linear models; random effects; Tweedie exponential dispersion model
⁰Email address: renjun@zeus.med.uottawa.ca